CN117724334A - Track tracking control method for single automatic bus-substituting parking robot - Google Patents

Track tracking control method for single automatic bus-substituting parking robot Download PDF

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CN117724334A
CN117724334A CN202311728865.5A CN202311728865A CN117724334A CN 117724334 A CN117724334 A CN 117724334A CN 202311728865 A CN202311728865 A CN 202311728865A CN 117724334 A CN117724334 A CN 117724334A
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parking
agv
parking agv
coordinate system
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谈东奎
吴雪波
朱波
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Hefei University of Technology
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Hefei University of Technology
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Abstract

The invention relates to a track tracking control method of a single automatic bus-substituting parking robot, which comprises the following steps: establishing a kinematic model of the parking AGV; establishing a dynamics model of the parking AGV; and designing a synovial membrane controller based on a nonlinear disturbance observer, taking a disturbance value estimated by the nonlinear disturbance observer as an input signal of the synovial membrane controller, converting the torque of a motor output by the synovial membrane controller into a motor rotating speed, outputting the motor rotating speed to a kinematic model of a parking AGV, and outputting the rotating speed required by four Mecanum wheels by the kinematic model of the parking AGV to realize track tracking control. According to the invention, firstly, the interference of the bearing universal wheels on the movement of the parking AGV is considered on the basis of analyzing the kinematic model of the parking AGV and the kinetic model of the parking AGV, the nonlinear disturbance observer is used for estimating the disturbance force and torque generated by the bearing universal wheels, and the non-singular terminal sliding film controller is combined to realize the tracking of the parking AGV to the reference track.

Description

Track tracking control method for single automatic bus-substituting parking robot
Technical Field
The invention relates to the technical field of intelligent control of a platform of a bus parking robot, in particular to a track tracking control method of a single automatic bus parking robot.
Background
In recent years, the automobile conservation amount in China is continuously increased, meanwhile, the land which can be developed and applied to the construction of parking lots in cities is continuously reduced, and a series of parking problems such as difficult finding of parking places, insufficient parking places, frequent occurrence of parking accidents and the like are increasingly developed. In order to be able to utilize as fully as possible the urban, severely limited parking space, safely and efficiently parking vehicles, more and more intelligent parking systems (Smart Parking System, SPS) are proposed. At present, intelligent parking systems can be divided into a direct type parking system and an indirect type parking system, namely, an automatic parking system (Automated parking systems, APS) is arranged on an intelligent vehicle, so that the vehicle automatically completes a parking task. The direct scheme has the advantages of more adaptive parking scenes and small requirements on parking lot infrastructures, but the method has the defects of limited space utilization rate of the parking lot and high requirements on the intelligent level of the automobile; secondly, the parking automatic guided vehicle (Automated guided vehicle, AGV) is utilized to automatically and indirectly complete the parking requirement, compared with APS, the AVP (Automated Valet Parking) system based on the parking AGV uses the parking AGV to automatically transport the vehicle, can realize the omnibearing movement to any position, and has no requirement on the intelligent level of the automobile; meanwhile, as the space for opening and closing the vehicle door and entering and exiting the vehicle is not required to be reserved for each parking space; compared with the traditional vehicle, the omnibearing parking AGV has strong maneuverability, so that the space utilization rate of a parking lot can be effectively improved; meanwhile, by means of the parking AGV, a user only needs to drive the vehicle to a parking lot connection area, so that the parking/taking time of the user can be saved, and the parking safety can be improved.
Currently, the AVP system based on the parking AGV has significant advantages and thus draws great attention from related researchers, and many types and forms of parking AGVs have been developed, in which the all-round motion clamp type parking AGV has been widely used because of the advantages of the tire clamping arm that can automatically clamp the wheels and lift the vehicle without any other equipment assistance.
On the basis of a parking AGV platform, researchers have conducted a great deal of research on the allocation, path planning and positioning of parking spaces, however, track tracking control of a parking AGV has received little attention, and although some research has been conducted on track tracking control of an omni-directional mobile parking AGV, track tracking control of a sliding mode control in an omni-directional mobile parking AGV has been widely applied, but influences of external disturbance on a control system are not considered in most cases, so that track tracking effects are poor and robustness is poor.
Disclosure of Invention
The invention aims to solve the problems of poor track tracking effect and poor robustness of an omni-directional mobile parking AGV, and provides a track tracking control method of a single automatic bus parking robot, which enables the parking AGV to accurately track an expected track, estimates and eliminates the influence of external disturbance on track tracking and improves the robustness in the tracking process.
In order to achieve the above purpose, the present invention adopts the following technical scheme: a trajectory tracking control method of a single automatic bus parking robot, the method comprising the sequential steps of:
(1) Establishing a kinematic model of the parking AGV;
(2) Establishing a dynamics model of the parking AGV;
(3) According to a kinematic model of the parking AGV and a kinematic model of the parking AGV, a synovial membrane controller based on a nonlinear disturbance observer is designed, disturbance values estimated by the nonlinear disturbance observer are used as input signals of the synovial membrane controller, torque output by the synovial membrane controller is converted into motor rotating speed, the motor rotating speed is output to the kinematic model of the parking AGV, and the kinematic model of the parking AGV outputs rotating speeds required by four Mecanum wheels to realize track tracking control.
The step (1) specifically refers to:
the parking AGV is a Mecanum wheel omnidirectional mobile platform, X w O w Y w Is the global coordinate system of the parking AGV; x is X v O v Y v A parking AGV body coordinate system; o (O) v Is the origin of coordinates of a parking AGV body coordinate system and is the center point of four Mecanum wheels; o (O) m Is the centroid of the parking AGV; v iw I=1, 2,3,4, v for the linear velocity of each mecanum wheel center iw ＝r m w iw ，r m Radius of Mecanum wheel, w iw Corresponding to the rotational angular velocity of each Mecanum wheel; v ir Tangential velocity of the ground-engaging rollers corresponding to each Mecanum wheel; w (w) z Yaw rate for a park AGVA degree; θ vw Obtaining an inverse kinematics equation of the parking AGV for the course angle of the parking AGV;
wherein: v x For the central speed of the vehicle body to be X v A speed component of the shaft; v y For the central speed of the car body to be Y v A speed component of the shaft; a is half of the center distance between the left and right transverse Mecanum wheels; b is half of the center distance between the front and rear Mecanum wheels longitudinally; the formula (1) is a kinematic model of the parking AGV;
formula (1) is rewritten to formula (2):
wherein:is the rotational angular velocity of the Mecanum wheel; />Wherein,and->Respectively lower edge X of parking AGV body coordinate system v 、Y v Is a velocity component of (a); />Yaw rate in a parking AGV body coordinate system;
the jacobian matrix J is defined as:
obtaining a forward kinematics equation of the parking AGV as follows;
wherein: j (J) + ＝(J T ·J) -1 ·J；
Establishing a coordinate transformation equation of a parking AGV body coordinate system and a global coordinate system, and obtaining the following coordinate transformation equation according to a motion relation:
wherein:wherein (1)>Respectively, parking AGVs under global coordinate system along X w ，Y w Is a velocity component of (a); />Yaw rate of the parking AGV in a global coordinate system; />R w2v (θ vv ) Represented by the following formula; θ vv The course angle is the course angle under the parking AGV body coordinate system;
combined formula (1) to formula (6) to obtainThe conversion relation between the speed of the parking AGV and the speed of the parking AGV is as follows;
wherein R (θ) vv ) Is a coordinate transformation matrix;
due to the origin O of the coordinates of the parking AGV v And centroid O m Theoretically, the parking AGV coordinate origin O is shown by the following formula after analysis v And centroid O m Velocity relationship between:
wherein:respectively is centroid O m Along X v ，Y v A speed component of the shaft; d, d x ，d y Respectively is centroid O m To the origin of coordinates O v Is a transverse and longitudinal distance of (2);
finally, the following formulas (5) to (8) are obtained;
the step (2) specifically refers to: the dynamics model of the parking AGV is established by adopting a Lagrange method, and a Lagrange function L of the parking AGV is obtained as shown in the following formula:
wherein: j (J) v AGVs wrap around Z for parking v The moment of inertia of the shaft; m is m v The mass of the whole car of the AGV is parked; j (J) w The moment of inertia of the Mecanum wheel;AGVs wrap around Z for parking w Yaw angle of shaftA speed; />Respectively, parking AGVs under global coordinate system along X w ，Y w Is a velocity component of (a); />Rotational angular velocity for each Mecanum wheel;
then, the method is combined with the method (9) and the method (10), and the Lagrangian function L is derived to obtain a dynamics model of the parking AGV, wherein the following formula is obtained:
wherein:
wherein,wherein->Respectively, parking AGVs under global coordinate system along X w ，Y w ，Z w Acceleration of (2); f (θ) vw )＝[F x F x T z ] T For generalized forces and moments, F x ，F y Respectively, parking AGV along X v ，Y v A generalized force component of the shaft; t (T) z AGVs wrap around Z for parking v Broad range of shaftSense moment, r m The radius of the Mecanum wheel is half of the center distance of the two Mecanum wheels on the left and right in the transverse direction; b is half of the center distance between the front and rear Mecanum wheels longitudinally; d, d x ，d y Respectively is centroid O m To the origin of coordinates O v Is a transverse and longitudinal distance of (2); θ vw For the course angle of the parking AGV +.>Yaw rate of the parking AGV in a global coordinate system; />For yaw rate in the parking AGV body coordinate system.
The step (3) specifically comprises the following steps in sequence:
(3a) Designing a nonlinear disturbance observer: the disturbing force and torque generated by all bearing universal wheels are synthesized into equivalent disturbing force and torque, which are expressed as:
F c ＝[F cx ，F cy ，T cz ] (15)
wherein: f (F) cx ，F cx X of AGVs along parking v ，Y v Equivalent disturbance force of the shaft; t (T) cz To wind Z of parking AGV v Equivalent disturbance torque of the shaft;
according to the dynamics model of the parking AGV, the generalized force and moment F (theta vw ) Further expressed as:
wherein:
wherein τ= [ τ ] 1 ,τ 2 ,τ 3 ,τ 4 ] T Is the driving moment of the Mecanum wheel; f= [ f 1 ,f 2 ,f 3 ,f 4 ] T For the friction force to which the mecanum wheel is subjected,F c additional equivalent disturbance forces and moments generated for the load-bearing universal wheels; θ vw For the course angle of the parking AGV, a is half of the center distance between the left and right transverse Mecanum wheels; b is half of the center distance between the front and rear Mecanum wheels longitudinally; /> Rotational angular velocity for each Mecanum wheel;
because of the centroid O of the parking AGV m Very close to the park AGV center O v Assuming the same load per Mecanum wheel, the friction force experienced by each Mecanum wheel is expressed as:
wherein: g is gravity acceleration; μ is the coefficient of friction between the mecanum wheel and the ground, taking μ=0.02; m is m v The mass of the whole car of the AGV is parked;
the nonlinear disturbance observer is expressed as:
wherein:
wherein z is an auxiliary variable;is disturbance force and torque F c Is a function of the estimated value of (2); c 0 ＝[c x ,c y ,c z ] T Tuning matrix of disturbance observer, c 0 ＝diag[1500,1500,150] T ；
Combined type (23) (24) to obtain L (q) vw ) The method comprises the following steps:
L(q vw )＝c 0 M(θ vw ) -1 (25)
defining observer error e 0 The method comprises the following steps:
assume that:
finally, the method comprises the following steps:
(3b) Designing a sliding film controller:
first, the tracking error is defined as:
wherein: q r ＝[x r ,y r ,θ r ] T The position information of the reference track in the global coordinate system; q vw The position information of the actual track in the global coordinate system; e, e x ,e y ,e θ Errors of X, Y direction and course angle under the global coordinate system respectively;
the sliding mode surface of the sliding film controller is designed to be the following formula:
wherein: p > q > 0 is a design parameter of the synovial membrane controller, and p/q < 2 is satisfied, p=5, q=3 is taken; χ=diag (χ) x ,χ y ,χ z ) Designing a matrix for a synovial controller, taking χ=diag (1.5,1.5,1.5);
deriving formula (30):
wherein:
and (3) obtaining the synovial membrane dynamics equation meeting the index approach rate:
wherein: e (E) s ,K s > 0 is the positive gain matrix of the switching surface of the synovial membrane controller, and E s Smaller approach speed is slower E s The larger the motion point reaches the switching surface, the larger the speed will be, the larger the shake caused is, and E is taken s ＝diag(0.5,0.5,0.5),K s ＝diag(1,1,1)；
Combined formula (29) and formula (30) to obtain:
finally, the combined formula (11), the formula (16) and the formula (31) are obtained:
according to the technical scheme, the beneficial effects of the invention are as follows: the invention provides a sliding film controller based on a nonlinear disturbance observer aiming at the track tracking problem of a parking AGV, firstly, the disturbance of a bearing universal wheel to the motion of the parking AGV is considered on the basis of analyzing a kinematic model of the parking AGV and a dynamic model of the parking AGV, the disturbance force and torque generated by the bearing universal wheel are estimated by using the nonlinear disturbance observer, and then the non-singular terminal sliding film controller is combined to realize the track tracking of the reference track of the parking AGV.
Drawings
FIG. 1 is a schematic diagram of the overall architecture of a parking AGV;
FIG. 2 is a block circuit diagram of a park AGV;
FIG. 3 is a kinematic model of a park AGV;
FIG. 4 is a schematic diagram of the architecture of a nonlinear disturbance observer-based synovial membrane controller;
FIG. 5 is a schematic diagram of a disturbance analysis of a load bearing gimbal;
FIG. 6 is a schematic diagram of a straight line tracking lateral error;
fig. 7 is a schematic diagram of circular tracking lateral error.
Detailed Description
A trajectory tracking control method of a single automatic bus parking robot, the method comprising the sequential steps of:
(1) Establishing a kinematic model of the parking AGV;
(2) Establishing a dynamics model of the parking AGV;
(3) According to a kinematic model of the parking AGV and a kinematic model of the parking AGV, a synovial membrane controller based on a nonlinear disturbance observer is designed, disturbance values estimated by the nonlinear disturbance observer are used as input signals of the synovial membrane controller, torque output by the synovial membrane controller is converted into motor rotating speed, the motor rotating speed is output to the kinematic model of the parking AGV, and the kinematic model of the parking AGV outputs rotating speeds required by four Mecanum wheels 10 to realize track tracking control.
The step (1) specifically refers to:
parking AGVs are typically Mecanum wheel omni-directional mobile platforms, as shown in FIG. 3, en route X w O w Y w Is the global coordinate system of the parking AGV; x is X v O v Y v A parking AGV body coordinate system; o (O) v Is the origin of coordinates of the parking AGV body coordinate system and is the center point of the four Mecanum wheels 10; o (O) m Is the centroid of the parking AGV; v iw I=1, 2,3,4, v for the linear velocity of each mecanum wheel center iw ＝r m w iw ，r m Radius of Mecanum wheel 10, w iw Corresponding to the rotational angular velocity of each mecanum wheel 10; v ir Tangential velocity of the ground-engaging rollers corresponding to each mecanum wheel 10; w (w) z Yaw rate for the park AGV; θ vw Obtaining an inverse kinematics equation of the parking AGV for the course angle of the parking AGV;
wherein: v x For the central speed of the vehicle body to be X v A speed component of the shaft; v y For the central speed of the car body to be Y v A speed component of the shaft; a is half of the center distance between the left and right transverse Mecanum wheels 10; b is half of the center distance of the front and rear Mecanum wheels 10 in the longitudinal direction; the formula (1) is a kinematic model of the parking AGV;
to facilitate subsequent trajectory control, formula (1) is rewritten as formula (2):
wherein:is the rotational angular velocity of the Mecanum wheel 10; />Wherein (1)>And->Respectively lower edge X of parking AGV body coordinate system v 、Y v Is a velocity component of (a); />Yaw rate in a parking AGV body coordinate system;
the jacobian matrix J is defined as:
obtaining a forward kinematics equation of the parking AGV as follows;
wherein: j (J) + ＝(J T ·J) -1 ·J；
For subsequent track tracking, a coordinate transformation equation of a parking AGV body coordinate system and a global coordinate system must be established, and according to a motion relation, the coordinate transformation equation is obtained as follows:
wherein:wherein (1)>Respectively, parking AGVs under global coordinate system along X w ，Y w Is a velocity component of (a); />Yaw rate of the parking AGV in a global coordinate system; />R w2v (θ vv ) Represented by the following formula; θ vv The course angle is the course angle under the parking AGV body coordinate system;
combined formula (1) to formula (6) to obtainThe conversion relation between the speed of the parking AGV and the speed of the parking AGV is as follows;
wherein R (θ) vv ) Is a coordinate transformation matrix;
due to the origin O of the coordinates of the parking AGV v And centroid O m Theoretically, the parking AGV coordinate origin O is shown by the following formula after analysis v And centroid O m Velocity relationship between:
wherein:respectively is centroid O m Along X v ，Y v A speed component of the shaft; d, d x ，d y Respectively is centroid O m To the origin of coordinates O v Is a transverse and longitudinal distance of (2);
finally, the following formulas (5) to (8) are obtained;
the step (2) specifically refers to: the dynamics model of the parking AGV is established by adopting a Lagrange method, and a Lagrange function L of the parking AGV is obtained as shown in the following formula:
wherein: j (J) v AGVs wrap around Z for parking v The moment of inertia of the shaft; m is m v The mass of the whole car of the AGV is parked; j (J) w Is the moment of inertia of the Mecanum wheel 10;AGVs wrap around Z for parking w Yaw rate of the shaft; />Respectively, parking AGVs under global coordinate system along X w ，Y w Is a velocity component of (a); />Rotational angular velocity for each Mecanum wheel;
then, the method is combined with the method (9) and the method (10), and the Lagrangian function L is derived to obtain a dynamics model of the parking AGV, wherein the following formula is obtained:
wherein:
wherein,wherein->Respectively, parking AGVs under global coordinate system along X w ，Y w ，Z w Acceleration of (2); f (θ) vw )＝[F x F x T z ] T For generalized forces and moments, F x ，F y Respectively, parking AGV along X v ，Y v A generalized force component of the shaft; t (T) z AGVs wrap around Z for parking v Generalized moment of shaft, r m The radius of the Mecanum wheel 10 is half of the center distance of the two Mecanum wheels 10 on the left and right sides in the transverse direction; b is half of the center distance of the front and rear Mecanum wheels 10 in the longitudinal direction; d, d x ，d y Respectively is centroid O m To the origin of coordinates O v Is a transverse and longitudinal distance of (2); θ vw For the course angle of the parking AGV +.>Yaw rate of the parking AGV in a global coordinate system; />For yaw rate in the parking AGV body coordinate system.
The step (3) specifically comprises the following steps in sequence:
in order to realize accurate tracking control performance and strong anti-interference robustness, a sliding mode controller based on a nonlinear disturbance observer is designed, the structure of the sliding mode controller is shown in fig. 4, the influence of disturbance force on track tracking is further analyzed on the basis of step (1) and step (2), the nonlinear disturbance observer is designed to estimate disturbance force and moment, and then a control method of the sliding mode controller based on the nonlinear disturbance observer is provided to track a reference track according to the designed disturbance observer. The parked AGVs of FIG. 4 include a kinematic model of the parked AGVs and a kinematic model of the parked AGVs.
Since the gripping arm of the parking AGV is equipped with the load bearing universal wheel 12, as shown in FIG. 5, when the curvature of the track of the parking AGV changes, the load bearing universal wheel 12 swings, and thus, additional disturbance force and moment are applied to the parking AGV, especially when the load is large, the influence cannot be ignored.
(3a) Designing a nonlinear disturbance observer: the disturbance forces and torques generated by all the load-bearing universal wheels 12 are synthesized into equivalent disturbance forces and torques, which are expressed as:
F c ＝[F cx ，F cy ，T cz ] (15)
wherein: f (F) cx ，F cx X of AGVs along parking v ，Y v Equivalent disturbance force of the shaft; t (T) cz To wind Z of parking AGV v Equivalent disturbance torque of the shaft;
considering the unknown dynamic disturbance force and friction force, according to the dynamics model of the parking AGV, the generalized force and moment F (theta vw ) Further expressed as:
wherein:
wherein τ= [ τ ] 1 ,τ 2 ,τ 3 ,τ 4 ] T Is the driving torque of the Mecanum wheel 10; f= [ f 1 ,f 2 ,f 3 ,f 4 ] T For the friction force to which the mecanum wheel 10 is subjected,F c additional equivalent disturbance forces and moments for the load-bearing universal wheel 12; θ vw For the course angle of the parking AGV, a is half of the center distance between the left and right transverse Mecanum wheels 10; b is half of the center distance of the front and rear Mecanum wheels 10 in the longitudinal direction; />Rotational angular velocity for each Mecanum wheel;
because of the centroid O of the parking AGV m Very close to the park AGV center O v Assuming the same load for each Mecanum wheel 10, the friction force experienced by each Mecanum wheel 10 is expressed as:
wherein: g is gravity acceleration; μ is the coefficient of friction between the mecanum wheel 10 and the ground, taking μ=0.02; m is m v The mass of the whole car of the AGV is parked;
in order to accurately estimate the disturbance forces and moments generated by the load bearing universal wheel 12, the proposed nonlinear disturbance observer is expressed as:
wherein:
wherein z is an auxiliary variable;is disturbance force and torque F c Is a function of the estimated value of (2); c 0 ＝[c x ,c y ,c z ] T Tuning matrix of disturbance observer, c 0 ＝diag[1500,1500,150] T ；
Combined type (23) (24) to obtain L (q) vw ) The method comprises the following steps:
L(q vw )＝c 0 M(θ vw ) -1 (25)
defining observer error e 0 The method comprises the following steps:
assume that:
finally, the method comprises the following steps:
(3b) Designing a sliding film controller:
the method comprises the steps of designing a sliding film controller to realize track tracking of the parking AGV and combining the sliding film controller with a nonlinear disturbance observer, wherein specifically, a disturbance value estimated by the nonlinear disturbance observer is used as an input signal of the sliding film controller, so that the robustness of track tracking of the parking AGV under uncertain disturbance is improved;
first, the tracking error is defined as:
e t ＝q vw -q r ＝[e x ,e y ,e θ ] T (29)
wherein: q r ＝[x r ,y r ,θ r ] T The position information of the reference track in the global coordinate system; q vw The position information of the actual track in the global coordinate system; e, e x ,e y ,e θ Errors of X, Y direction and course angle under the global coordinate system respectively;
the sliding mode surface of the sliding film controller is designed to be the following formula:
wherein: p > q > 0 is a design parameter of the synovial membrane controller, and p/q < 2 is satisfied, p=5, q=3 is taken; χ=diag (χ) x ,χ y ,χ z ) Designing a matrix for a synovial controller, taking χ=diag (1.5,1.5,1.5);
deriving formula (30):
wherein:
and (3) obtaining the synovial membrane dynamics equation meeting the index approach rate:
wherein: e (E) s ,K s > 0 is the positive gain matrix of the switching surface of the synovial membrane controller, and E s Smaller approach speed is slower E s The larger the motion point reaches the switching surface, the larger the speed will be, the larger the shake caused is, and E is taken s ＝diag(0.5,0.5,0.5),K s ＝diag(1,1,1)；
Combined formula (29) and formula (30) to obtain:
finally, the combined formula (11), the formula (16) and the formula (31) are obtained:
as shown in fig. 1, the parking AGV body is composed of a frame 1, a rear clamping arm 2, a front clamping arm 3, four mecanum wheels 10, two push rod motors 7, a push rod motor fixing base 8, four traveling motors 9, a coupler 11 and the like, when the parking AGV moves to the bottom of an automobile, the rear clamping arm 2 transversely moves and expands under the drive of a rear expanding motor 13, the front clamping arm 3 is folded and expanded under the drive of a front expanding motor 6, wherein the front clamping arm 3 is fixed on a sliding block 5 through bolts, the sliding block 5 can move on a guide rail 4, and finally, the front clamping arm 3 and the rear clamping arm 2 clamp the automobile tire and jack up the automobile with the aid of the push rod motors 7; while the load bearing universal wheels 12 under the clamping arms bear the majority of the weight of the car.
As shown in fig. 2, the laser radar and the inertial navigation sensor upload the point cloud data and the data such as the direction angle/yaw rate of the parking AGV to the industrial personal computer respectively, the industrial personal computer builds a map of the surrounding environment according to the data, then the industrial personal computer sends pose information of the AGV to the electronic control unit ECU, and the electronic control unit ECU sends a torque signal to the motor driver according to a corresponding control strategy, so as to control the parking AGV to move according to the planned track.
The invention aims at the problem of tracking the track of the parking AGV, and provides a sliding film controller based on a nonlinear disturbance observer. As shown in fig. 6 and 7.
In summary, the invention provides a sliding film controller based on a nonlinear disturbance observer aiming at the track tracking problem of a parking AGV, firstly, the disturbance of a bearing universal wheel to the motion of the parking AGV is considered on the basis of analyzing a kinematic model of the parking AGV and a dynamics model of the parking AGV, the nonlinear disturbance observer is used for estimating the disturbance force and torque generated by the bearing universal wheel, and then the non-singular terminal sliding film controller is combined to realize the track reference track of the parking AGV.

Claims (4)

1. A track tracking control method of a single automatic bus-in parking robot is characterized in that: the method comprises the following steps in sequence:
(1) Establishing a kinematic model of the parking AGV;
(2) Establishing a dynamics model of the parking AGV;
(3) According to a kinematic model of the parking AGV and a kinematic model of the parking AGV, a synovial membrane controller based on a nonlinear disturbance observer is designed, disturbance values estimated by the nonlinear disturbance observer are used as input signals of the synovial membrane controller, torque output by the synovial membrane controller is converted into motor rotating speed, the motor rotating speed is output to the kinematic model of the parking AGV, and the kinematic model of the parking AGV outputs rotating speeds required by four Mecanum wheels to realize track tracking control.
2. The trajectory tracking control method of a single automatic valet parking robot according to claim 1, wherein: the step (1) specifically refers to:
the parking AGV is a Mecanum wheel omnidirectional mobile platform, X w O w Y w Is the global coordinate system of the parking AGV; x is X v O v Y v A parking AGV body coordinate system; o (O) v Is the origin of coordinates of a parking AGV body coordinate system and is the center point of four Mecanum wheels; o (O) m Is the centroid of the parking AGV; v iw I=1, 2,3,4, v for the linear velocity of each mecanum wheel center iw ＝r m w iw ，r m Radius of Mecanum wheel, w iw Corresponding to the rotational angular velocity of each Mecanum wheel; v ir Tangential velocity of the ground-engaging rollers corresponding to each Mecanum wheel; w (w) z Yaw rate for the park AGV; θ vw Obtaining an inverse kinematics equation of the parking AGV for the course angle of the parking AGV;
wherein: v x For the central speed of the vehicle body to be X v A speed component of the shaft; v y For the central speed of the car body to be Y v A speed component of the shaft; a is half of the center distance between the left and right transverse Mecanum wheels; b is half of the center distance between the front and rear Mecanum wheels longitudinally; the formula (1) is a kinematic model of the parking AGV;
formula (1) is rewritten to formula (2):
wherein:is the rotational angular velocity of the Mecanum wheel; />Wherein (1)>Andrespectively lower edge X of parking AGV body coordinate system v 、Y v Is a velocity component of (a); />Yaw rate in a parking AGV body coordinate system;
the jacobian matrix J is defined as:
obtaining a forward kinematics equation of the parking AGV as follows;
wherein: j (J) + ＝(J T ·J) -1 ·J；
Establishing a coordinate transformation equation of a parking AGV body coordinate system and a global coordinate system, and obtaining the following coordinate transformation equation according to a motion relation:
wherein:wherein (1)>Respectively, parking AGVs under global coordinate system along X w ，Y w Is a velocity component of (a); />Yaw rate of the parking AGV in a global coordinate system; />R w2v (θ vv ) Represented by the following formula; θ vv The course angle is the course angle under the parking AGV body coordinate system;
combined formula (1) to formula (6) to obtainThe conversion relation between the speed of the parking AGV and the speed of the parking AGV is as follows;
wherein R (θ) vv ) Is a coordinate transformation matrix;
due to the origin O of the coordinates of the parking AGV v And centroid O m Theoretically, the parking AGV coordinate origin O is shown by the following formula after analysis v And centroid O m Velocity relationship between:
wherein:respectively is centroid O m Along X v ，Y v A speed component of the shaft; d, d x ，d y Respectively is centroid O m To the origin of coordinates O v Is a transverse and longitudinal distance of (2);
finally, the following formulas (5) to (8) are obtained;
3. the trajectory tracking control method of a single automatic valet parking robot according to claim 1, wherein: the step (2) specifically refers to: the dynamics model of the parking AGV is established by adopting a Lagrange method, and a Lagrange function L of the parking AGV is obtained as shown in the following formula:
wherein: j (J) v AGVs wrap around Z for parking v The moment of inertia of the shaft; m is m v The mass of the whole car of the AGV is parked; j (J) w The moment of inertia of the Mecanum wheel;AGVs wrap around Z for parking w Yaw rate of the shaft; />Respectively, parking AGVs under global coordinate system along X w ，Y w Is a velocity component of (a); />Rotational angular velocity for each Mecanum wheel;
then, the method is combined with the method (9) and the method (10), and the Lagrangian function L is derived to obtain a dynamics model of the parking AGV, wherein the following formula is obtained:
wherein:
wherein,wherein->Respectively, parking AGVs under global coordinate system along X w ，Y w ，Z w Acceleration of (2); f (θ) vw )＝[F x F x T z ] T For generalized forces and moments, F x ，F y Respectively, parking AGV along X v ，Y v A generalized force component of the shaft; t (T) z AGVs wrap around Z for parking v Generalized moment of shaft, r m The radius of the Mecanum wheel is half of the center distance of the two Mecanum wheels on the left and right in the transverse direction; b is half of the center distance between the front and rear Mecanum wheels longitudinally; d, d x ，d y Respectively is centroid O m To the origin of coordinates O v Is a transverse and longitudinal distance of (2);θ vw for the course angle of the parking AGV +.>Yaw rate of the parking AGV in a global coordinate system; />For yaw rate in the parking AGV body coordinate system.
4. The trajectory tracking control method of a single automatic valet parking robot according to claim 1, wherein: the step (3) specifically comprises the following steps in sequence:
(3a) Designing a nonlinear disturbance observer: the disturbing force and torque generated by all bearing universal wheels are synthesized into equivalent disturbing force and torque, which are expressed as:
F c ＝[F cx ，F cy ，T cz ] (15)
wherein: f (F) cx ，F cx X of AGVs along parking v ，Y v Equivalent disturbance force of the shaft; t (T) cz To wind Z of parking AGV v Equivalent disturbance torque of the shaft;
according to the dynamics model of the parking AGV, the generalized force and moment F (theta vw ) Further expressed as:
wherein:
wherein τ= [ τ ] 1 ,τ 2 ,τ 3 ,τ 4 ] T Is the driving moment of the Mecanum wheel; f= [ f 1 ,f 2 ,f 3 ,f 4 ] T For the friction force to which the mecanum wheel is subjected,F c additional equivalent disturbance forces and moments generated for the load-bearing universal wheels; θ vw For the course angle of the parking AGV, a is half of the center distance between the left and right transverse Mecanum wheels; b is half of the center distance between the front and rear Mecanum wheels longitudinally; /> Rotational angular velocity for each Mecanum wheel;
because of the centroid O of the parking AGV m Very close to the park AGV center O v Assuming the same load per Mecanum wheel, the friction force experienced by each Mecanum wheel is expressed as:
wherein: g is gravity acceleration; μ is the coefficient of friction between the mecanum wheel and the ground, taking μ=0.02; m is m v The mass of the whole car of the AGV is parked;
the nonlinear disturbance observer is expressed as:
wherein:
wherein z is an auxiliary variable;is disturbance force and torque F c Is a function of the estimated value of (2); c 0 ＝[c x ,c y ,c z ] T Tuning matrix of disturbance observer, c 0 ＝diag[1500,1500,150] T ；
Combined type (23) (24) to obtain L (q) vw ) The method comprises the following steps:
L(q vw )＝c 0 M(θ vw ) -1 (25)
defining observer error e 0 The method comprises the following steps:
assume that:
finally, the method comprises the following steps:
(3b) Designing a sliding film controller:
first, the tracking error is defined as:
e t ＝q vw -q r ＝[e x ,e y ,e θ ] T (29)
wherein: q r ＝[x r ,y r ,θ r ] T The position information of the reference track in the global coordinate system; q vw The position information of the actual track in the global coordinate system; e, e x ,e y ,e θ Errors of X, Y direction and course angle under the global coordinate system respectively;
the sliding mode surface of the sliding film controller is designed to be the following formula:
wherein: p > q > 0 is a design parameter of the synovial membrane controller, and p/q < 2 is satisfied, p=5, q=3 is taken; χ=diag (χ) x ,χ y ,χ z ) Designing a matrix for a synovial controller, taking χ=diag (1.5,1.5,1.5);
deriving formula (30):
wherein:
and (3) obtaining the synovial membrane dynamics equation meeting the index approach rate:
wherein: e (E) s ,K s > 0 is the positive gain matrix of the switching surface of the synovial membrane controller, and E s Smaller approach speed is slower E s The larger the motion point reaches the switching surface, the larger the speed will be, the larger the shake caused is, and E is taken s ＝diag(0.5,0.5,0.5),K s ＝diag(1,1,1)；
Combined formula (29) and formula (30) to obtain:
finally, the combined formula (11), the formula (16) and the formula (31) are obtained:
CN202311728865.5A 2023-12-15 2023-12-15 Track tracking control method for single automatic bus-substituting parking robot Pending CN117724334A (en)

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